Solving an Equality in Quantum Mechanics: Help Needed!

In summary, the conversation discusses an equality found in a book involving complex conjugation. The person is confused about the second equality and questions why it holds. The other person clarifies by pointing out that the notation is just written differently and the last equality does indeed hold.
  • #1
Niles
1,866
0

Homework Statement


Hi

Please take a look at the following equality found in my book:

[tex]
\left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle } = \sum\limits_v {\left\langle {\mu }
\mathrel{\left | {\vphantom {\mu v}}
\right. \kern-\nulldelimiterspace}
{v} \right\rangle ^* \left| v \right\rangle }
[/tex]

The asterix denotes complex conjugation. I cannot see why the second equality holds, since

[tex]
\sum\limits_v {\left\langle {\mu }
\mathrel{\left | {\vphantom {\mu v}}
\right. \kern-\nulldelimiterspace}
{v} \right\rangle ^* \left| v \right\rangle } = \sum\limits_v {\left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle \left| v \right\rangle } \ne \sum\limits_v {\left| v \right\rangle \left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle }
[/tex]

What am I missing here?


Niles.
 
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  • #2
Why don't you think the last equality holds? You're just writing <v|u>, which is a number, behind |v> instead of in front of it.
 
  • #3
Yeah, you are right. Thanks.
 

FAQ: Solving an Equality in Quantum Mechanics: Help Needed!

How do I solve an equality in quantum mechanics?

Solving an equality in quantum mechanics involves using mathematical techniques such as linear algebra and differential equations to manipulate the equations and find a solution that satisfies the conditions of the equality. This can be a complex process and may require knowledge of advanced mathematics.

What are some common techniques for solving an equality in quantum mechanics?

Some common techniques for solving an equality in quantum mechanics include using operators and eigenvalues, solving for the wave function, and using the Schrödinger equation. It is also important to have a strong understanding of quantum mechanics principles and concepts.

How do I know if my solution to an equality in quantum mechanics is correct?

To determine the correctness of a solution to an equality in quantum mechanics, the solution should satisfy all of the conditions and constraints of the problem. It should also be consistent with the principles and laws of quantum mechanics.

What are some tips for effectively solving an equality in quantum mechanics?

Some tips for effectively solving an equality in quantum mechanics include breaking the problem down into smaller, more manageable steps, practicing and gaining a strong understanding of the necessary mathematical techniques, and seeking help from a mentor or tutor if needed.

Are there any resources available for help with solving equalities in quantum mechanics?

Yes, there are many resources available for help with solving equalities in quantum mechanics. These include textbooks, online tutorials, study groups, and academic support services offered by universities. It is also helpful to seek guidance from knowledgeable peers or professors.

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